January 29, 2013- added Perfect Tetris- Apoc's input- Why you should learn this

Part 1

Hello all.

You may have seen or heard of me. But allow me tell you who I am anyways. I am anonymous, the best downstacker on all of Hard Drop!

Okay, that may not be 100% true. If you're judging by downstacking speed, Apocalypse is the best downstacker, but if you're judging by efficiency, then I am confident in saying that I am the best downstacker*!

*Only in terms of Blockbox. If you're not familiar with Blockbox. Basically, it's all completely messy garbage, and double sends 1 line, triple sends 2 lines, tetris sends 4 lines, and Back to Back also adds an extra line send (so B2B tetris sends 5 lines). Also, there are no spins and no combos.

NOTE: This part is stuff about Blockbox strategy. If you don't want to read about Blockbox strategy, then skip down to the downstacking section, although I encourage you to read this part as it may give you some good insight into downstacking.

So before I begin, we should define what efficiency is. I determine efficiency in terms of three things:

- lines built up- lines sent- lines downstacked

The basic gist of my definition is lines built up vs lines sent and lines downstacked. I consider a line sent and a line downstacked to be of equal value (this isn't always true, but for simplification, they're of equal value).

Anyways, Here's a table showing the efficiency of all the different line clears. For efficiency, I did efficiency = (lines sent + lines downstacked) / lines built. In the table, I labeled back to back as b2b and garbage clears as g [line clear]. I realize that the math is slightly inaccurate since I didn't take into account the little block that goes into the garbage line, but a long time ago, I did the math and took into account the little block, and the results are pretty much the same, so bear with me.

According to the table, the most efficient things you can do are (in this order):

What does this tell us? None garbage line clears are bad, and theoretically, you should maximize garbage singles. Here is the most efficient game you can play:

Clearly, this situation is highly unlikely, and actually impossible to do with the bag system. Theoretically though, this placement is what you should be striving for.

Personally though, I don't try to follow this strategy. The above strategy is way too difficult to achieve.

The basis of my strategy is that every clear must include a garbage line. This means (theoretically) no regular singles, no regular doubles, triples or tetrises. You can only get garbage singles, garbage doubles, etc.

Going more in depth, my main strategy is to keep my field as clear as possible through garbage clears. If your field is clear, it's easy to stack on and easy to keep clear (or at least easier than if your field was jaggedy). So how do you keep your field clear? Getting garbage doubles! Garbage doubles are excellent for three reasons. They have the second highest efficiency, if you do them (right) they keep your field nice and clean which also allows you to get garbage singles, and you don't really have to look down your field so much. Here's a pretty typical dig race 10 lines game I play:

Sorry I don't know how to make previews on fumen

Of course, you won't always be able to get just garbage singles and doubles. Often times you'll have to get garbage triples, garbage tetrises, and even *shivers* regular singles, although these aren't necessarily bad things, just try to minimize them if you can.

My strategy is much better than the one above because my strategy, while difficult, is still achievable and efficient.

Anyways, I hope this has been insightful, or at least interesting for you. But, enough talk about Blockbox! You're here to learn how to downstack, not Blockbox strategy!

Why you should learn this (January 29, 2013)

I know there are some people who tell themselves, "Why do I want to learn how to play Blockbox style? I only play TF/Nullpomino/TOP/etc. I don't play Blockbox at all, and I don't plan on playing it. Blockbox garbage is too hard! I only need to get better at downstacking TF garbage, not Blockbox garbage."

To begin, don't be a little girl and say Blockbox garbage is too hard (no offense to any little girls reading this). It's not hard. The problem is that you haven't put an effort into understanding downstacking. You play for a few hours, maybe even a few days and decide it's too hard. Instead of trying to learn how to downstack it, you scoff at it and say "why should I learn how to do it"? Well, this is exactly the wrong mindset to have if you ever want to be a good player.

Instead of saying that "Blockbox is dumb" or "this is too hard", focus on the real truth. You're bad at downstacking. However, there's absolutely nothing wrong with being bad at downstacking because it means you have room for improvement. If you have the mindset that "downstacking is too hard" as opposed to "I am bad at downstacking", then you already have the idea that you can't be good at downstacking. However, if you think to yourself "I am bad at downstacking" then at least you understand that you can improve (In fact, this applies for a lot of things, not just downstacking).

Having said that, downstacking is very tough to learn and only few players properly learn to downstack. You don't get any tangible feedback that you're getting better at downstacking. But I can tell you that if you practice these techniques, then you will improve your downstacking.

Furthermore, think about the long run benefits. If you can learn to downstack this garbage, you can learn to downstack anything thrown at you in TF. Sure, when you start, you may struggle (a lot) with the garbage, but once you understand it, then it'll just become natural to you. Also, games like TF will become a lot easier for you.

Think about this. American Football players practice running with a parachute behind them so that they can run faster when they're in game. Tetris is no different. If you can downstack Blockbox garbage, then you can downstack anything on TF and Nullpo.However, Blockbox teaches you more than just how to downstack. I can tell you that playing Blockbox has helped me become a better player in TOJ/TF/Nullpo in more ways than just becoming a good downstacker. Playing Blockbox has also helped me stack cleaner and flatter without needing to skim much, and it has helped me increase my combos.

Yes, playing Blockbox will greatly increase your downstacking ability, but it also increases your stacking ability as well. When you have 90% random garbage, you have to make lots of decisions, like where should I place my pieces so that I block the next garbage hole the least? What piece fits best in my garbage hole? What is my next garbage hole going to look like? Is the piece I need for the next garbage hole coming up or do I need to change what it looks like? A whole plethora of questions that require lots of analyzation in only brief moments. *

When you become good at these things, and you play TF and Nullpo, it really shows. Because TF/Nullpo's garbage isn't as messy, you don't have to worry as much about stacking over upcoming garbage holes, what piece you're going to need etc. The end result is that your stack becomes cleaner which allows you to build more T-spins, you can upstack faster, you have more time to think, and it allows you to downstack faster.

Furthermore, playing Blockbox style (or at least my style) is excellent for increasing your average combo. In my style, you basically are trying to turn all the singles and doubles you are getting into bigger line clears. For instance:

So how is this related to comboing? Well, comboing is just the exact opposite. Instead of turning singles and doubles into larger line clears, you're trying to turn those larger line clears into a lot more smaller line clears. In other words, comboing is just the exact opposite of my style.

It may seem paradoxical that I say playing my style has helped me combo better since they're pretty much opposites. However, the reality is, when you play my style, it gives you an excellent understanding of piece placement which can increase your combos by an extra one or two. This may not seem like a lot, but going from a combo 4 to a combo 6 sends an extra six lines (depending on what game you play), and if you consistently do this multiple times throughout the game, then you've increased your apm by 6-12 (or possibly more) depending on how much you do it.

Also, I know a lot of people will read this thread in hopes that there is some secret that makes you an incredible downstacking. But, I'm here to tell you that there is no secret to becoming a pro downstacker.

The only thing you can do is consciously practice playing efficiently (either my style or at the very least trying to use the least number of pieces). Playing normally is not enough. If you want to be good, you must actively train your mind to see the best ways to downstack.

* But keep in mind, Blockbox doesn't teach you how to do everything. Watching your opponent's field, choosing when you want to accept or cancel garbage, choosing when you should attack or when you should defend/play passively are skills you'll have to learn on your own when you play TF.

Downstacking Techniques

Here I'll be posting some general stuff on downstacking that helped me become the player I am today!

There are a few techniques I use when downstacking. The first technique, I showed in the first post. I'll call it the "Garbage Double Technique" If anyone can think of a better name, please give me one because I'm terrible at making names.

Garbage Double:

The basic premise is that you just get a bunch of garbage doubles, and you get garbage singles if you can. The main point of this is to keep your field clear and try to avoid any garbage Tetrises, garbage Triples, and most of all non garbage line clears. (Although to be honest, garbage Tetrises and garbage Triples are still good and I get them a lot) Anyways, garbage doubles are good because they keep your field clear so you can keep getting more garbage doubles. Since your field is clear, you can get more garbage singles, and the cycle of g goubles and g singles repeats (hopefully). Clear field means easy to stack on, which will allow you to do whatever you want. You can keep downstacking, or if you see your opponent is about to die, you can stack up, or you can make an easy t-spin, etc.

So how do you learn how to do this? I suggest you play dig race 10 lines and at the beginning of the game, try to get as many garbage doubles as you can. 18 lines and you'll feel pressured at the top, 5 lines isn't enough. You could also play dig challenge. Personally, I learned how to do this by practicing this at the beginning of every survivor game (or dig challenge if you play Nullpomino). People complain that the beginning part of survivor/dig challenge is too slow, but this is the perfect opportunity to attempt this. You can try getting garbage doubles at the beginning of the games and then when the game starts going fast, you just downstack regularly.

Here's an examples of me doing it.

I piece placement

Everyone knows that on games like Blockbox, the I piece is the most important piece there is. And, I completely agree, but for different reasons than most people.

Most people see I pieces as nothing more than something to make Tetrises. Some people see them as a way to alleviate bad stacking habits, like this:

But I pieces are useful for a wide variety of things, such as making Tetrises, or more importantly downstacking. Say what?! The I piece is good for downstacking? Yes! The I piece basically gives you one free line clear that can open up many options for you. For example, in my Specific Downstack section, the very first example uses an I piece to downstack.

Also, you should know that if you get that one free line clear, it should ONLY be used for garbage lines, and not lines that you built up. For instance, this is good:

This is bad:Actually I can't think of a good situation. If I do, I'll put a fumen down, but for now, goo.

The I piece is also good if you have a messy field, having an I piece will allow you to stack up and fix your field. A lot of the time, players have a messy field, and then they stack up to fix their field, but they don't keep in mind to have an I piece, and they end up stacking 5-6 lines.

green lines denote stuff you've already built up.

I pieces are good for getting rid of excess pieces on your field too:

One thing you have to watch out for though, is stacking an I piece over a close by upcoming garbage hole that.

In conclusion, I pieces are the shiznit. They allow you to fix your messy fields, they let you clear excess pieces on your field so you can keep it clean, and in general it provides a lot of flexibility in downstacking.

Predicting your hole

Another fundamental downstacking technique is predicting your hole. In order to be a good downstacker, you have to know what your next garbage hole is going to look like. Here's an example:

As you can see, I know that the hole is going to need an I, L, or J piece, so I hold one of those pieces. And then I use it when the time comes!

To be pro, you also need to know how to change your hole. Obviously, you can't change where your next garbage hole is. But, you can change what you want your hole to look like, and what your next garbage hole is going to look like too. The second part of this sentence "what your next garbage hole is going to look like" is especially crucial. One mistake I see many people make is that they don't foresee what their next hole is going to look like. This is EXTREMELY important; not just in downstacking, but in creating prophecy t-spins and other advanced techniques. Here's some examples of me changing the garbage hole.

ugh, messed up the fumen. Frame 21 to 24, I only had 1 S piece, not 2 in a row.

Note that when I "change" the hole, I know exactly what I'm doing. I planned out that whole sequence in my head. I saw that I didn't have a good piece sequence to downstack through those holes, and I saw that if I put the S piece there, I would need a J piece. However, there was a J piece coming up in my preview so I changed the hole. After that, it's just a matter of filling in the rest of the field so I don't get any wasted singles and stuff.

In this game, I say that I have no upcoming T piece, and then a T piece comes along, but just pretend I didn't have a T piece coming up lol.

A lot of my technique is recognizing what shapes your garbage holes are going to form and holding the piece you need. Then once you have the piece you need, you just fill in the field so that you don't waste any lines with singles. And, if you have an unfavorable piece sequence, then you change the hole so that you do have a favorable piece sequence.

Stacking Flat Over Holes

When downstacking, the one thing everyone says is "don't stack over the holes". However, I think a better philosophy is "don't stack over the holes... but if you do, stack flat over the holes". Why do you stack flat over the next holes? So that when you clear your current garbage line, your next garbage hole is open.

Furthermore, if you have a flat stack over your next hole as opposed to just not stacking over holes, you'll have more ways to downstack the hole.

Here's an example of me stacking flat over holes

Downstacking Rhythm

Sometimes when you downstack, you have The Feeling. You're downstacking like a pro! You clear through 8 lines in 4 seconds! And then, suddenly you mess up and you lose your downstack mojo. I see this a lot when I watch people downstack. They downstack a few holes, and then they get stuck on one hole for a long time. You lose your rhythm, and then you either lose the game, or it takes you a while to recover back to your normal state.

So what causes players to lose this downstack mojo? There are two main situations: awkward stacks/piece placements, and having a block over your hole.

Block over your hole:

For example, here's a game of me playing dig race:

Notice how at some points I have a block over the hole. However, I fill in the rows until the single block over the hole is gone.

And here's a game where you downstack 4 lines and then have a block over your hole:

This is the kind of thing I was talking about at the beginning of the section. Many people downstack 4 holes and then they meet block over the hole and are temporarily setback. And then in those few moments, they lose a lot of position, time, or even the game.

So how do you stop this? Just fill in the rows so that you don't have a block over your hole. You can also think about it like this. However many blocks you have over that garbage hole, you have to clear that many lines. This is a very important concept, and when I finally understood this, I improved my downstacking skills a lot faster and became pro.

Also take note that I say "clear at least 3 lines or more". You can also build up one more line (so you've built up a total of 4 lines) and get a garbage Tetris, which is technically more efficient. But, for me, I'd rather not take the risk of building up excess lines which could make my stack uneven or possibly cause me to have to get a single, so I just get the garbage triple.

Vipjun pointed out to me that after he realized this, he could visualize his field a lot better. I'm not going to try to type out/explain our discussion because then you'll just get really confused, but hopefully this picture will be sufficient.

This section also works well with "stacking flat over holes", so keep that in mind!

Knowing when to stack up

In general, you want to keep your field empty and clean, but there are times where keeping your stack low is bad. Specifically, whenever you reach garbage holes that are stacked, that means you need to start building up because when lines are next to eachother and on top of eachother, putting down pieces can block upcoming garbage holes. Like this:

When the holes are like this, you've got to start building up lines to plow through the garbage holes. If they're in a column of 2, then build a 2 column hole around them. If they're in a column of 3, then build a 3 column hole. If they're in 4 different columns, then it gets slightly more difficult. When they're in 4 column holes, then it's pretty much the same as 3 column, but with a slight twist which is confusing to explain, but hopefully you will see it in the fumen.

When I say "be cautious how many lines you build" in frame 15. I mean that however many garbage holes are stacked, that's how many lines you have to build up. So, in frame 15, within the 3 column well, you have 3 stacked holes, so you want to build up 3 lines. If you build up 4 lines, then you'll have one line left over which will cause you to get an unnecessary single.

Also, I realize I have a section in the "specific downstacking part", but this needed more analysis.

EDIT: I was playing a game of dig race 10 lines and did this:

Reversing holes

I can't believe I forgot this. It's so simple, but it's such a key concept to understand. Here is what hole reversing is/how to do it:

Notice the T can reverse both sides. This is one reason why the T piece is such a valuable piece. Not only does it fix jaggedy stacks and does t-spins; it also reverses your hole, which is essential when downstacking. T pieces have so much flexibility so it's important to hold T pieces whenever you can (I pieces too!).

It's important for you to see future situations where you need to reverse your hole. For instance, if you create a situation on the left side of the well in the fumen. When you clear the right side, you'll be left with a block over your garbage hole. So you need to reverse it. Depending on the orientation of the blocked hole, you can use a J or T, or a L or T.

Also, you should reverse the hole before you start clearing the lines. So in the fumen, I should reverse the left side before I get the Tetris (or whatever line clear) on the right. That way, I don't have to get a single later on.

A lot of people forget that L and J pieces can reverse holes too. For instance, in frame 1, a lot of people only see that the T can reverse the blocked hole. However, you need to see that you can use the T or L piece, since this effectively doubles the chance you get the piece you need so you can downstack quicker. (And you can save that T piece for something else like a T spin).

Hole reversing is an incredibly easy technique to understand, yet I see many people don't do it or aren't good at it. However, I definitely recommend learning it because it's such an easy concept to understand and learn and it can increase your downstacking and adding skill by a pretty good margin for such an easy technique.

Eventually when you start recognizing when you need to reverse holes, you can do advanced stuff like this:

Consecutive Downstacking

In an earlier section, I talked about what happens when you have holes stacked over each other. Well, sometimes, when the holes are not stacked over each other (i.e. spread apart*), you can choose to downstack many holes (3-4) at once, and then turn the last garbage hole into a large line clear. This can be very efficient if you can get 3 garbage singles, and then a garbage Tetris. For instance:

*Actually you can almost always use Consecutive Downstacking, but it's a lot easier to do when the holes are spread apart.

What makes consecutive holes? Mainly, the first thing is that the holes are not stacked together. Even if the holes are spread relatively far, if two of the holes are stacked, or near stacked, you'll be in trouble if you're trying to downstack using Consecutive Downstacking (see frame 2). Then, the second thing to see is, how spread out are the holes. The more spread out the holes are, the easier it is to use Consecutive Downstacking, since spread out holes means you have more options to place your pieces (see frame 4).

There are two important aspects to do Consecutive Downstacking. The first important aspect is looking for spread holes, and then set a goal. If I see I can downstack consecutive garbage lines, then I'll set my goal to the 3rd, 4th, or 5th hole (or whatever the last hole I think I can reach is). After that, the other important thing behind downstacking consecutive holes is to not stack over future holes. Here's another example:

One hindrance to Consecutive Downstacking is that you can really only do it if your field is relatively clear. If you have a lot (or even a few) lines stacked up, then you won't be able to use this technique. But if you're using garbage doubles and the other techniques, then having a clear field isn't too difficult.

Learning to recognize when you can do this can take a while, but it can help a lot in games like TF where you rarely receive single lines of garbage, but when you do, the garbage comes in consecutive lines of 3-5 (because of combos and doubles). And when this happens, and the lines are favorable for consecutive downstacking, you can just plow through the lines and get down to your straight line garbage easily.

Consecutive Downstacking is also good if you're trying to play dig race and use the least amount of pieces (although I recommend playing to be efficient rather than using least pieces).

Perfect Tetris: (March 15, 2012)

If you ever watch pros play, a lot of the times, they'll stack up a perfect 4 lines and get that tetris, and people will be amazed at how they always manage to stack up a perfect 4 lines, get a Tetris, and leave the next garbage hole uncovered.

How do they do it? There are certain Tetris Indicators to indicate how many lines they need to build up. For instance in this example, when you put the J piece in, it forms a perfect 4 lines:

Pros can instantly recognize these Tetris Indicators, place in the appropriate piece, and then not have to worry about counting how many lines they need to build up. They only have to watch to make sure that they stack up to fill at least that many lines. For example, in the previous fumen:

This can be extremely useful when there is a Tetris Indicator over a garbage hole, since once you put the piece in, you only have to worry about filling in and not stacking over the next garbage hole.

Here are some other Tetris Indicators:

Here's something that's particularly useful when your stack is a little bit messy (or even when it's normal) and you have a pyramid.

Also for anyone who hasn't seen apocalypse's blockbox survivor video, you're missing out!

If you watch, he keeps his field flat and clear pretty much the whole time which is why he can downstack so fast!

Also, words from Apocalypse:

QUOTE

First off, I would like to thank anonymous for posting my video as an example, I feel honored...Also, I am not as "techy" or smart as these guys, giving such support to the topic, but my opinion is that good down-stacking isn't something you develop with just practice like stacking fast. Fast stacking requires lots of practice because you familiarize certain patterns, you might not be conscious of it but its memorized, you have more control over that. Down-stacking in the other hand requires a lot of improvisation, you receive garbage that you cannot predict or control(unless you are a uber nerd and have the formula for it). For good down-stacking you MUST enter that mindset of seen the lower gaps in relation to your incoming pieces and see the best possible way of using these(which is something "duh").

I had to play thousands of games to enter that mindset, survivor mode really helped me a lot and I feel there are way better down-stackers out there, my speed is a huge factor to my down-stacking, people like meow, radiance, anonymous and trance(which I'm sure there are more people but these guys are coolest imo) that have such efficiency down-stacking that makes my speedy down-stacking look foolish, they might give you the key to "entering the mindset".

I like anonymous input on keeping the field flat for an easier down-stacking, Blink keeps a nice flat field which makes it easier for him to set up combos and clear garbage, probably one of the best at it. Meow with his patience guided me to understanding that important factor(hes the guy you should seek if this is an issue for you as it was for me).

I know I probably talked a lot of bs and said things you already know, but I didn't understand these things myself, I kept playing and playing and playing with desperation, believing I would suddenly be good at it.

Another important aspect of downstacking is thinking of your pieces as combinations of pieces. I think I posted something about this somewhere. Someone was asking about stacking techniques. The basic gist was to think of stacking up in terms of block combinations that fit well together, such as J and Z; L and S, JZL, etc.

Downstacking is also very similar in that you should think of your pieces in terms of piece combinations. Here's one example I do a lot. At the end, I use an I piece and a J piece together to downstack the two garbage holes.

(This isn't the only thing you could have done in this situation, but I'm just saying, this comes up a lot when I play).

These piece combinations are important to learn because once you know them, you can see recognize the garbage holes and be like, oh, I know what to do in this situation. And, when you recognize the pieces you need, you can plan ahead for the next garbage holes.

Specific Part 2:

Here's a fumen of a basic, mid level, and high level downstacking example.

Specific Part 3:

Sometimes, you're close to the top, and you can't afford to wait for pieces "the right pieces" for the garbage hole. In these cases, you'll have to get some singles and change what your hole looks like.

Also note, in the last few frames, i get a double instead of two singles. If you're trying to make a combo chain, you can just get the two singles instead of the double to increase your chain by one.

Specific Part 4:

Don't you hate it when all the garbage holes are right next to each other?! Anyways, here's one way I deal with them:

Note that this doesn't apply only when the holes are near the wall. This technique works almost as well even if the holes are in the middle. It's slightly harder to do this though because you have to split your stack into two; but it's still pretty effective.

Specific Part 5:

This one doesn't really have to do with downstacking, but it comes in handy every once in a while.

Plus, it's a pretty sweet move!

Specific Part 6:

Specific Part 7:

Here's a situation that I occasionally see.

The key thing to see in this fumen is that I have two consecutive garbage holes next to each other, and over the current garbage hole, I have three blocks stacked over it. When you put in the I piece, it leaves a J (or L depending on hole orientation) shaped hole.

Specific Part 8:Here's a technique I do a lot. A LOT.

For example, here's a game of me playing dig race:

Stuff you should NOT do

I'll also be posting stuff that I see a lot of people do, but are bad.

Don't Part 1:

The reason why frames 1-3 is bad is because in your current position (frame 1), you have 1 block over your current garbage hole. When you put the Z piece in, you clear 2 lines, but you still have to one block over your current hole. However now, you're actually in worse position than before. In frame 1, you only need 1 piece to get to your garbage hole. However, in frame 3, you need to build 2 more lines (approximately 5 pieces) just to get back into the position you were in before so you can put in the T piece, or IJ, or LJ.

You can get around the infinity problem by making efficiency = (garbage sent + garbage cleared)/(pieces used). This is something I've been referring to as "throughput" in the past. It paints a more accurate picture of how "efficient" each attack is. I expand the idea by adding another statistic: flux. You can be efficient as hell, but if you're not fast enough, you'll lose. Flux takes this into account. Flux = (garbage sent + garbage cleared)/(minutes played), or simply throughput*TPM. In a previous thread, meow kind of independently used this (but in a different way), and agreed with it. Although, I just can't seem to get the Nullpo devs to implement these stats ;].

Anyway, here's the throughput chart for Blockbox (the right side is sorted by throughput):

Although, deciding what to do in a real game to maximize your throughput over the whole game is actually more complicated than simply trying to do what's on that chart. This is something I've been working on for a while and actually have a big chunk of an article typed up to explain it all. I need to get around to finishing that up...

Fun fact: this idea was first written about around ten years ago by legendary player spindizzy on his site.

Oh yeah, I remember reading your posts about throughput, but I never understood it until now.

Originally, when I was doing the math a year and a half ago, I did use "pieces used" instead of "lines built". However, when I tried explaining it to people, they got confused, so I just changed it to lines built for ease.

I definitely would like to see "Flux" or something similar added as a stat. It'd make it a lot easier to judge your skill rather than just estimating skill from tpm, apm, and lpm. Even if it's not 100% accurate, it would give a lot more insight into your play style, and it'd still be better than having just apm, lpm, and tpm.

A garbage single is infinity because it clears 1 garbage line and it takes 0 lines to build (because you only use one piece to do it).

Obviously, this is flawed. It was fixed before as I said above when I used "pieces used" instead of "lines built" but it confused some people so I changed it. Unfortunately "lines built" still confused people.

Here is an idea that supports efficiency, with the help of some algebra. My idea is to take a game with some specific properties, and instead of analyzing it as a whole, just look at some of the basic properties that can be derived by-passing (that is, not using) a lot of stuff that goes in the actual game logic.

I hope I haven't made a big blunder somewhere in this argument or reasoning since I tend to struggle with clarity on algebra of both inequalities and propositions.

Well anyway, the conditions I have placed are somewhat strict. Some of these can be eased up or changed, while others are necessary.

1- The game would play with rhythm controls. For example, at the end of each frame, simply the input given is checked and the block is based in field based on the input.2- The garbage sent is usual as in normal games but no spin bonus. 3- The garbage would be with one hole but garbage positioning doesn't matter. There is no garbage canceling. Also, the game starts without any garbage. 4- The game immediately when the garbage lines reach the top. But the players may place as many blocks above the field as they want to.

Conditions 3 and 4 are important while 1 and 2 can be relaxed. In any case this point would be better explained towards the end of this post.

Note that whenever I use the term block, I actually mean just one block (or one fourth of a tetromino). This simplifies a lot of unnecessary confusion. Now at the end of each frame we take note of certain values. For example, we keep running totals of the following values:t = time in frames

G1 = total garbage blocks sent by the first playerB1 = total non-garbage blocks cleared by the first playerD1 = total garbage blocks cleared by the first player

Similarly we can define analogous values for the second player. Now we can also define two more values which are related to what is present on the field at a given time.

GB1 = number of garbage blocks present in the first player's field at a given timeK1 = number of non-garbage blocks present in the first player's field at a given time

We can also define the same values for the second player in a similar way. Now the following relation is clear:GB1 = G2 - D1 where G2 > D1

Coming to the efficiency of a specific move, every specific move can be defined by three values, which are g, b, and d. Note that when talking about these values for a specific move, it is better to use lower case letters to avoid confusion. For example, few values for clears would be:1- Singlesa- g=0, b=1, d=92- Doublesa- two garbage linesg=9, b=2, d=18b- one garbage lineg=9, b=11 d=9c- no garbage lineg=9, b=20 , d=03- Triplesa- three garbage lineg=18, b=3, d=27b- two garbage linesg=18, b=12, d=18c- one garbage linesg=18, b=21, d=9d- no garbage lineg=18, b=30, d=04- Tetris a- four garbage linesg=36, b=4, d=36b- three garbage linesg=36, b=13, d=27c- two garbage linesg=36, b=22, d=18d- one garbage lineg=36, b=31, d=9e- no garbage lineg=36, b=40, d=0

Similarly, we can also do this for b2b tetrises. Those frames where we put a block and don't clear a line, or where we simply don't do anything can also be characterized as moves. The former case changes the value of K. If we don't want to characterize these as moves, it doesn't really matter much, as long as we increase our time counter correctly. The point is that these moves don't enter the calculation for efficiency.5- g=0, b=0, d=0

At the end of each frame, the running totals of G, B and D are updated. Based on the game logic, the values for GB and K are updated too. After the first player performs a move with values g1,b1,d1 (values g2,b2,d2 for the second player) during t-->t+1 cycle, the values are updated as

Now we want to see that when does a player win the game. Based on the way we defined our gameP: GB1 >= 180Q: GB2 >= 180

Consider the four possibilities that result:A- P and Q both trueThe game ends in a drawB- P true and Q falseThe second player winsC- P false and Q trueThe first player winsD- P false and Q falseThe game is going on

Before we move on to draw some conclusions a simple point about efficiency would be helpful. We can define efficiency of a sequence of two moves as:e=(b1*e1+b2*e2)/(b1+b2)Of course this way we can extend it to any sequence of moves. Notice that for moves with g=b=d=0 it doesn't matter what value we give to efficiency (0 is a good number anyway). Those moves won't add anything to the calculation of the running value of e.

1- In which cases possibility A can't occur for a game?For A to occur we must have had a frame where values of GB1 and GB2 both increased (this is a necessary condition). This in-turn means that moves performed in the particular cycle were such that: g2 - d1 > 0 andg1 - d2 > 0

Now we check all pairs of moves we have. This condition is true (both individual conditions that is) for some pairs so we canít conclude that A canít occur. Well we can intuitively see it can. However, if it wasnít true for any pair of moves we have, we could say without appealing to game logic that A canít occur. In our particular game, A can occur.

Now the next point is really important and this is what, in my opinion, highlights the importance of efficiency.

2- If both players place pieces at the same average rate (when the game ends with one player winning) and:a- the first player plays more efficientlyb- has less or equal unused non-garbage blocks in the field, compared to the second playerThen we can say for sure, without looking at the game, that the first player has won.

To show this, consider the possibility C. For it to be true, we must have:GB1=G2-D1<180 and GB2=G1-D2>=180which means that-GB1>-180A necessary but not sufficient condition for the two inequalities above to be true is:GB2-GB1>0 (notice that minimum would be 180-179=1)or we can write(G1-D2)-(G2-D1)>0(G1+D1)-(G2+D2)>0By using E1=(G1+D1)/B1E2=(G2+D2)/B2 we can re-write this as:B1*E1-B2*E2>0orGreater: B1*E1>B2*E2

Similar analysis would show that the necessary condition for possibility B is:Less: B1*E1<B2*E2

If both players played with the same average rate, at the point when one of them won, they must have placed equal blocks in the field up-till that point. Let the total blocks placed be T. Then clearly we have the relations:T = B1+K1 --> B1=T-K1T = B2+K2 --> B2=T-K2Re-writing the above inequality B1*E1-B2*E2>0:(T-K1)*E1-(T-K2)*E2>0

Since we are already given K1 <= K2, we have-K1 >= -K2T-K1 >= T-K2

We are also given E1>E2. This means that B1*E1>B2*E2 is true. Now since the game has ended, we know that we are in either B or C. Since B1*E1>B2*E2 is true in C and false in B, this means that we must be in C.

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Few more discussion points:1- If we define:Greater: B1*E1>B2*E2Equal: B1*E1=B2*E2Less: B1*E1<B2*E2

then I think this is how these possibilities would occur in different possible states defined above.A -- Less, Equal, GreaterB -- LessC -- GreaterD -- Less, Equal, Greater

2- Let the analogous values for tpm, lpm and apm be R, L and A respectively. In that case, we would have:R1=(B1+K1)/tL1=(B1+D1)/tA1=G1/t

These values and tpm, lpm, apm only differ by a multiplication constant.

3- We can define time efficiency as:TE= E / t = (G+D)/(B*t)In all the above statements we can essentially replace efficiency by time efficiency. Essentially it calculates the G+D factor balanced against blocks used and time taken, so it provides a way to measure useful play without reference to time taken. What caffeine is referring to as flux then would be:F = B*TE

Is F a better measure or TE? I am not sure, but if someone was dying many times with unused non-garbage blocks F would hold it against the player. TE, on the other hand, would just see how effectively the player is using the blocks that are actually used for making lines.

4- It doesn't really matter if the game has rhythm controls or not. The game logic might be more complex but we could still divide all frames, where no lines are made, into two categories:a- one where no tetromino is placed.b- one where a tetromino is actually placed on the field, as part of it.

5- So efficiency is really a measure that can be used in a more general sense, and not just downstacking. It doesnít matter if we allow spins bonuses or not. All we would have to do would be to declare and detect spins as different moves from doubles or triples.

How much garbage cancellation would skew this measure or how to mitigate or resolve this skewing would be a good investigation point.

Another thing is that even if both players were playing synchronously (so the playing speed would be a non-factor), the local most efficient move isn't necessarily the best one, as was pointed out before. Essentially one would guess that everything would matter, from the player's field, to randomizer, hold or even the opponents playfield, and essentially this would have to be re-evaluated after every placement.